{
  "id": "1507.03317",
  "version": "v1",
  "published": "2015-07-13T03:22:02.000Z",
  "updated": "2015-07-13T03:22:02.000Z",
  "title": "The spectrum of the growth rate of the tunnel number is infinite",
  "authors": [
    "Kenneth L. Baker",
    "Tsuyoshi Kobayashi",
    "Yo'av Rieck"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In a previous paper Kobayashi and Rieck defined the growth rate of the tunnel number of a knot $K$, a knot invariant that measures the asymptotic behavior of the tunnel number under iterated connected sum of $K$. We denote the growth rate by $\\mbox{gr}_t(K)$. In this paper we construct, for any $\\epsilon > 0$, a hyperbolic knots $K \\subset S^{3}$ for which $1 - \\epsilon < \\mbox{gr}_t(K) < 1$. This is the first proof that the spectrum of the growth rate of the tunnel number is infinite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-13T03:22:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "57M25"
    ],
    "keywords": [
      "tunnel number",
      "growth rate",
      "first proof",
      "knot invariant",
      "paper kobayashi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703317B"
    }
  }
}